RE: Sum of 1/Primes

*To*: mathgroup at smc.vnet.net*Subject*: [mg36973] RE: [mg36910] Sum of 1/Primes*From*: "DrBob" <drbob at bigfoot.com>*Date*: Thu, 3 Oct 2002 05:33:25 -0400 (EDT)*Reply-to*: <drbob at bigfoot.com>*Sender*: owner-wri-mathgroup at wolfram.com

No, Euler proved that series divergent in 1737. It's the usual theorem used to show that while the primes are sparse, they're not as sparse as the squares (as the sum of THEIR inverses converges). Bobby -----Original Message----- From: Matthias.Bode at oppenheim.de [mailto:Matthias.Bode at oppenheim.de] To: mathgroup at smc.vnet.net Subject: [mg36973] [mg36910] Sum of 1/Primes Dear Colleagues, I calculated: Sum[1/Prime[n], {n, 15000}] // N Result: 2.74716 Now I wonder if this sum will converge or keep on growing, albeit very slowly. Best regards, Matthias Bode Sal. Oppenheim jr. & Cie. KGaA Koenigsberger Strasse 29 D-60487 Frankfurt am Main GERMANY Tel.: +49(0)69 71 34 53 80 Mobile: +49(0)172 6 74 95 77 Fax: +49(0)69 71 34 95 380 E-mail: matthias.bode at oppenheim.de Internet: http://www.oppenheim.de